Photometric phase functions of common geologic minerals and applications to quantitative analysis of mineral mixture reflectance spectra

Abstract

Hapke's model for bidirectional reflectance is used to calculate the mass fractional abundance of components in intimately mixed, particulate surfaces from laboratory reflectance spectra. Application of this model, simplified by the assumptions that all surfaces scatter light with the same constant phase function and the opposition surge is negligible, to binary mineral mixtures are summarized and compared with new results for ternary mixtures of olivine, enstatite, and anorthite. These experimental tests indicate that the simple model is accurate to within 7% for mixtures not containing low albedo components (<10% reflectance). However, several observed systematic deviations of the calculated mass fractions from the actual mass fractions suggest that the simple model may be improved by allowing for variable scattering between the minerals used. An empirical scattering function, based on the physically plausible scattering behavior that low albedo materials are backward scattering and high albedo, transparent materials are forward scattering, reduces the magnitude of the systematic deviations in mass fractions observed with the constant scattering model. To determine if the empirical scattering function is representative of the actual scattering behavior of particulate mineral surfaces, specific photometric parameters (single‐scattering albedo, single‐particle phase function) of five different mineral components (olivine, enstatite, anorthite, magnetite, hematite) and two mineral mixtures (90% olivine 10% magnetite, 25% olivine 75% magnetite) are derived from bidirectional reflectance spectra measured at 17 different viewing geometries between 0.5 and 1.6 μm. Mineral components were crushed and wet sieved with ethanol to a 45 to 75 μm particle size. All reflectance data are corrected for the non‐Lambertian scattering properties of halon. Analysis of the parameters of the single‐particle phase function indicate that each mineral defines a relatively unique suite of scattering parameters as a function of albedo. In particular, the silicates are forward scattering where the degree of forward scattering increases with albedo, magnetite is forward scattering but the degree of forward scattering decreases with albedo, and hematite is entirely backward scattering where the degree of backward scattering increases with albedo. It is apparent that the physical properties of the particles (roughness, transparency, shape) rather than albedo or chemical composition determine the gross scattering properties of the particulate surfaces studied here. The scattering parameters of the mixtures are similar to the parameters of the more abundant mineral in the mixture. The experimentally determined single‐scattering albedos are used to calculate the mass fractions of olivine and magnetite in these mixtures. These new fractions are much improved over the previous analyses and indicate that more detailed information regarding the geometric dependence of reflectance overcomes the systematic deficiencies of the simplified methods. In general, the simplified method is appropriate for mixtures not containing low albedo material using bidirectional reflectance measured at intermediate phase angles (20°–40°) and small emergence angles (near 0°). Abundance estimates using this approach are accurate to within 5–10% when information regarding the particle size of the surface components is available, and in a relative sense for surfaces of unknown particle size distributions. More precise abundance estimates can be derived if the scattering properties of the surface are well characterized and incorporated into the analysis.